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j.engstruct.2018.08.031

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Engineering Structures 175 (2018) 86–100
Contents lists available at ScienceDirect
Engineering Structures
journal homepage: www.elsevier.com/locate/engstruct
Wind-induced responses of tall buildings under combined aerodynamic
control
T
⁎
Chaorong Zhenga,b, , Yu Xieb, Mahram Khanb, Yue Wua,b, Jing Liuc,d
a
Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin 150090, China
School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China
c
Heilongjiang Provincial Key Laboratory of Building Energy Efficiency and Utilization, Harbin 150090, China
d
School of Architecture, Harbin Institute of Technology, Harbin 150090, China
b
A R T I C LE I N FO
A B S T R A C T
Keywords:
Tall building
Wind-induced response
Combined aerodynamic control
Shape optimization
Air suction
The new trend towards constructing taller buildings makes modern tall buildings be increasingly susceptible to
wind excitations. Therefore, a combined aerodynamic control, including the shape optimization of the crosssection (passive aerodynamic control) and air suction (active aerodynamic control), is put forward to achieve a
more considerable reduction of the wind-induced responses of a tall building with square cross-section, so as to
improve its wind-resistance performance. Firstly, based on the wind excitations acquired by wind tunnel test of
four suction controlled tall building models with different cross-sections (consists of the square, corner-recessed
square, corner-chamfered square and Y-shaped cross-sections, and are denoted as Models 1–4 respectively), the
wind-induced responses of the prototype tall buildings and simplified mass-spring models are calculated using
the time history analysis method. Secondly, effects of the suction flux coefficient CQ, shapes of the cross-sections
and wind direction angles θ on the characteristics of the wind-induced responses are analyzed. The results show
that the combined aerodynamic control is very effective in reducing the along-wind and across-wind responses at
most cases, however, it can sometimes be unfavorable to the torsional responses. Among the four tall buildings,
Model 2 has the best performance in the along-wind direction, with a maximum reduction of the extremum tip
displacement of 34% caused by the shape optimization, and 29% caused by the air suction and a total of 63%
caused by the combined aerodynamic control at a relatively low CQ (CQ = 0.0159). However, the regularity is
quite different for the across-wind responses; when θ is equal to 0°, the maximum reduction of the extremum tip
displacement in the across-wind direction caused by the shape optimization and air suction are 49% for Model 4
and 47% for Model 1 respectively. Finally, a quantitative discussion on the reduction of the wind-induced
responses of tall buildings caused by the combined aerodynamic control is conducted, which can provide a
valuable reference for further studies or potential engineering applications.
1. Introduction
During the past decades, with the advances in high-strength and
light-weight structural materials, and new generation of structural
systems and construction technologies, tall buildings with increased
height and complicated shape have been continuously built up.
Generally, tall buildings of this kind have reduced structural mass,
stiffness, and damping ratio. And hence, they are usually very susceptible to wind excitations, which have the potential to reduce their
structural safety or cause discomfort to the occupants [1–3]. Therefore,
how to reduce the wind loads and wind-induced responses, so as to
ensure acceptable performance for survivability, serviceability and
habitability, is of great concern for the researchers and engineers in
wind engineering.
According to the vibration control theory, there are mainly three
kinds of measures adopted to mitigate the wind-induced responses
[4,5]:
(1) Structural measures: Recent development of advanced structural
systems, such as bundled tubes, belt trusses, outrigger trusses,
vierendeel-type bandages and mega frame systems etc., significantly increase the structural mass, stiffness and natural frequency of tall buildings [5,6].
(2) Damping measures: Incorporation of auxiliary damping devices
⁎
Corresponding author at: Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin 150090,
China.
E-mail address: flyfluid@163.com (C. Zheng).
https://doi.org/10.1016/j.engstruct.2018.08.031
Received 15 January 2018; Received in revised form 13 July 2018; Accepted 11 August 2018
0141-0296/ © 2018 Elsevier Ltd. All rights reserved.
Engineering Structures 175 (2018) 86–100
C. Zheng et al.
changes in its cross-section. In some cases, the change in cross-section
over the building height can be achieved through smoother modifications by twisting movements (as for example in the case of Shanghai
Tower, completed in 2016, which is twisted by 120°, shown in Fig. 1c).
Despite the enormous advantages that can be acquired by the passive aerodynamics control, inherent limitations make the aerodynamic
shape tailoring not always sufficient to reach the desired response level.
Generally, the aerodynamic shape tailoring can only reduce the drag
force and base moment less than 25% [16], and the reduction of the tip
displacement and acceleration are usually less than 30% and 15% respectively [17].
In order to improve the robustness of the passive aerodynamic
control and to further reduce the wind loads and wind-induced responses, several active aerodynamic control measures, such as the oscillating surface [18], moving surface boundary-layer control (MSBC)
[19], aerodynamic flap system [20,21], traveling wave wall [22], and
air suction or blowing [23–26] etc. to generate virtual modification of
building shapes, were proposed. Suction control, which was first utilized by Prandtl [27] to control the flow separation of a circular cylinder, has been proved to be a very effective means to control the
vortex shedding for numerous flow configurations, such as the airfoil
flows [24,28], the compressor cascade flows and the backward-facing
step flows [23,29], and to improve the wind-resistance performance for
high-rise buildings [25,26] and bridges [30]. The basic principle of
suction control is to restrain the flow separation and vortex shedding of
a bluff body by absorbing the low-speed flows in the boundary layer
[31,32], resulting in a significant reduction of aerodynamic forces.
In our previous work, CFD simulation [26], wind tunnel test [33],
and PIV (Particle Image Velocimetry) experiment [34] were conducted
to systematically investigate the characteristics of wind loads of tall
buildings controlled by air suction and to explore the mechanism of
suction control. However, a more promising trend is to combine the
passive and active aerodynamic control, so as to achieve a more considerable control effect over the wind loads and wind-induced responses, and also avoid their individual disadvantages (such as the inherent limitations of the passive aerodynamic control and large energy
input for the active aerodynamic control). Therefore, in the present
paper, a combined aerodynamic control (consists of the shape optimization of the cross-section and air suction) are put forward to reduce the
wind-induced responses of a tall building. And effects of the suction flux
[7–9], including the passive dampers (such as the steel damper,
viscous damper, Tuned Mass Dampers (TMD), Tuned Liquid Dampers (TLD), etc.) and active dampers (such as the Active Mass
Dampers (AMD), Hybrid Mass Dampers (HMD), Active Variable
Stiffness (AVS), etc.), into tall buildings to enhance their capacity of
dissipating energy.
(3) Aerodynamic measures: Improving the aerodynamic performance
of tall buildings via passive aerodynamic control or active aerodynamic control to reduce wind excitations.
The passive aerodynamic control, such as implementing shape optimization of the cross-section [10–12], modifications of the cross-section along the height [13,14], and vertical or horizontal through
building openings [10] etc. to generate the aerodynamic shape tailoring, is a powerful means to achieve optimal wind-resistance performance for tall buildings [15]. Modifications of the cross-sectional
shape, as for example the inclusion of recessed corners, chamfered
corners, horizontal slotted corners and Y shape [1,11], have been found
to considerably reduce the wind loads and wind-induced responses of
tall buildings, in comparison to those of a basic square cross-sectional
tall building. As for the longitudinal modifications, the inclusion of
setback, tapering and helical shapes, the progressive elimination of
corners or rotation of cross-section with the height not only are characteristics of some of the most graceful and notable buildings, but also
have been demonstrated to have a practical aerodynamic purpose
[13,14].
Some recent examples have shown that the passive aerodynamic
measures that create aerodynamically efficient forms can be integrated
into the design of tall buildings without sacrificing their appearance.
For example, in the case of the Taipei 101 Tower, completed in 2004
(Fig. 1a), every group of eight floors constitutes a tapered segment,
creating a pattern that recalls important cultural symbolism and enhancing at the same time the aerodynamic performance [3]. As is illustrated by Irwin [16], the double recessed corners can generate a 25%
reduction of base moment for the Taipei 101 Tower. More recent
structure with setbacks along the height is the Burj Khalifa Tower,
completed in 2010 (Fig. 1b) with a height of 828 m, which holds the
record of the tallest building in the world. In particular, in this case, the
influence of vortex-induced excitations was minimized by deterring the
formation of a coherent wake structure, through frequent and drastic
Fig. 1. (a) Taipei 101 Tower, (b) Burj Khalifa Tower, (c) Shanghai Tower.
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Engineering Structures 175 (2018) 86–100
C. Zheng et al.
is defined as 0° when the wind direction is perpendicular to the windward face.
coefficient, different cross-sections and wind direction angles on the
wind-induced responses are analyzed to quantitatively discuss the reduction of the responses generated by the passive, active and combined
aerodynamic control respectively. Section 2 is mainly concerned on
setup of the wind tunnel test for a tall building model controlled by the
combined aerodynamic measures, and Section 3 presents the time history analysis method to calculate the wind-induced responses of tall
buildings. Characteristics of the wind-induced responses of the tall
buildings in the along-wind, across-wind and torsional directions are
analyzed in Section 4. And Sections 5 and 6 show discussions and the
main conclusions.
2.2. Suction control system
As is shown in Fig. 4, the suction control system mainly consists of
three parts: two internal suction pipes inside the test model (see
Fig. 4b), pump system (includes a pair of vortex fans, flowmeters and
flow control valves) and external connections (includes the steel wire
reinforced hoses and PVC pipes). Each internal suction pipe, which
envelopes the suction air through the suction hole, is linked to the steel
wire reinforced hose and then connected to the pump system.
According to our previous research [26,39], the suction flux coefficient CQ, which is defined by Eq. (1), is the most important parameter
to dominate the suction control effect.
2. Wind tunnel test setup
The wind tunnel test is carried out in the Joint Laboratory of Wind
Tunnel and Wave Flume located at Harbin Institute of Technology,
China. The dimensions of the small test section are 25.0 m in length, 4.0
m in width and 3.0 m in height. A digital pressure measurement system
DSM 3400 (SCANIVALVE Corp., America) is used to synchronously
measure the multi-point pressures on scaled models with a sampling
frequency of 625 Hz, and the total time of each measurement is 60 s.
Three one-dimensional hot wires (DANTEC Corp., Denmark) are used to
measure the wind speed.
CQ = ρc Qc/(ρ∞ Q∞) = ρc dUc h/(ρ∞ D′UH H )
(1)
where ρc and ρ∞ are the density of the suction air and the oncoming air
(ρc = ρ∞ = 1.225 kg/m3) respectively; Qc and Q∞ are the flux of the air
suction through one suction hole and the oncoming air respectively;
while Uc and UH are the suction speed normal to the side face and the
oncoming wind speed at top of the test models, and UH is set as 7 m/s in
this paper. Therefore, the Reynolds numbers based on maximum projecting width of each model and the top wind speed are about
8.07 × 104, 7.39 × 104, and 8.50 × 105 for Model 1, Models 2–3, and
Model 4 respectively.
The suction speed Uc and corresponding CQ for different test models
are listed in Table 1.
2.1. Test models
Four tall building models, including a square model, corner-recessed
square model, corner-chamfered square model and Y-shaped model
(abbreviated as Models 1–4 respectively, and Model 1 is defined as the
baseline model), are adopted as the test models. The scaled models have
a same height of 600 mm (H = 600 mm) but different shapes of the
cross-section. The geometric scale ratio of the scaled models is set as
1:300, so the height of the prototype tall building is 180 m. The corner
recession/chamfering ratio of Models 2–3 are determined to be 10%,
because these models have the best wind-resistance performance
compared to other corner recession/chamfering ratios (such as 5% and
15%) based on our CFD simulations [33], and the results agree well
with Zhang et al.’s experimental results [35] and other previous results
[11,16,36].
Dimensions of the four cross-sections, which are designed to have a
same usable floor area according to Tse et al.’s suggestion [37], are also
shown in Fig. 2. It can be seen that the windward face widths (D) for
Model 1, Models 2–3, and Model 4 are 118 mm, 120 mm, and 62 mm
respectively, and the maximum transverse width (D′) for Model 4 is 177
mm, so the blockage ratio of the wind tunnel is less than 5%. To
measure wind pressure around surfaces of the test models, there are 16,
26, 22 and 27 pressure taps distributed on the cross-sections of Models
1–4 with ten height levels, so the total number of pressure taps are 160,
260, 220 and 270 respectively. More detailed information about the
arrangement of pressure taps on the test models can be found in Zhang’s
thesis [38].
The dimensions of each suction hole, which is symmetrically located
at each side face of the model with a distance of 10%D to its leading
separation edge (see Figs. 2 and 3), is 400 mm in height (from the
height 200 mm to 600 mm in Fig. 2, h = 400 mm) and 5 mm in width
(d = 5 mm). Location of the suction holes (i.e. 10%D) is determined
based on the comprehensive consideration of two aspects: Firstly, according to our previous research [26,39]), the control effect will be
better if the suction hole is closer to the leading separation edge; secondly, the distance between the suction hole and the leading separation
edge should be long enough so that it is feasible to fabricate the internal
suction pipes inside the test model.
Fig. 3 shows the schematic diagram of the suction control on the
square cross-section and definition of the wind direction angle. It can be
seen that the suction angle is defined as 90° when the direction of air
suction is perpendicular to the side face, and the wind direction angle θ
2.3. Wind field simulation
The terrain roughness at the building site is assumed to be the exposure category C in the Chinese load code GB 50009-2012 [40], and
the mean wind speed profile and turbulence intensity profile below the
gradient wind height (zG = 450 m) can be expressed as
U (z ) = UH (z / H )0.22
(2)
Iu (z ) = I10 (SL·z /10)−0.22
(3)
where UH is the reference wind speed at top of the test models, z is the
height above ground of the wind tunnel, SL equals to 300 is the reciprocal value of the geometric scale ratio between the scaled model
and the prototype tall building (see Section 3.2), and I10 is the turbulent
intensity at a height of 10 m, set as 0.23 for the exposure category C.
The passive devices, including the roughness elements, spires, a
serrated barrier and a carpet (More detailed information can be found
in Zhang [38]), are used to simulate the wind field in the wind tunnel.
3. Wind-induced responses analysis method
3.1. Newmark method
Analysis of wind-induced responses of a tall building is to solve the
motion equilibrium equation (Eq. (4)) of the structure.
mu¨ (t ) + cu̇ (t ) + ku (t ) = p (t )
(4)
where m, c and k are the mass, damping constant and stiffness of the
structure respectively, u (t ), u̇ (t ) and u¨ (t ) are the displacement, velocity
and acceleration of the structure respectively, and p(t) is the wind excitation.
Newmark method is a time-stepping method to solve the motion
equilibrium equation using Eqs. (5) and (6).
u̇i + 1 = ui + [(1−γ )Δt ] u¨ i + (γ Δt ) u¨ i + 1
ui + 1 = ui + (Δt ) u̇i +
[(0.5−β )(Δt )2] u¨
(5)
i
+
[β (Δt )2] u¨
i+1
(6)
where ui (ui + 1), u̇i (u̇i + 1) and üi (üi + 1) are the displacement, velocity, and
88
Engineering Structures 175 (2018) 86–100
C. Zheng et al.
Fig. 2. Dimensions (Unit: mm) and schematic diagrams of the test models: (a) square model, (b) corner-recessed square model, (c) corner-chamfered square model,
(d) tapered model, and (e) Y-shaped model.
Table 1
Arrangement of test cases.
Test model
Uc (m/s)
CQ
θ (°)
Square model
0,
6,
0,
0,
6,
0,
0,
6,
0,
0,
6,
0,
0, 0.0081, 0.0161, 0.0203,
0.0242, 0.0323, 0.0365
0, 0.0242, 0.0365
0, 0.0079, 0.0159, 0.0198,
0.0238, 0.0317, 0.0356
0, 0.0238, 0.0356
0, 0.0079, 0.0159, 0.0198,
0.0238, 0.0317, 0.0356
0, 0.0238, 0.0356
0, 0.0054, 0.0108, 0.0135,
0.0162, 0.0216, 0.0243
0, 0.0162, 0.0243
0
Corner-recessed square
model
Corner-chamfered square
model
Y-shaped model
2,
8,
6,
2,
8,
6,
2,
8,
6,
2,
8,
6,
4,
9
9
4,
9
9
4,
9
9
4,
9
9
5,
5,
5,
5,
Fig. 3. Schematic diagram of the suction control and wind direction angle.
Fig. 4. Suction control system: (a) pump system and external connections, (b) internal suction pipes.
89
15, 30, 45
0
15, 30, 45
0
15, 30, 45
0
15, 30,
45, 60
Engineering Structures 175 (2018) 86–100
C. Zheng et al.
2.0x106
Start
1.5x106
1
β Δt 2
Fxj (N)
Input the force P(t); time step
t ; structure information
[K], [M], [C]; value of ,
a =
0
Level 3
Level 7
1
γ
,a =
,a =
1 βΔt 2 βΔt
1.0x106
5.0x105
1
Δt γ
γ
a =
- 1, a = - 1, , a =
( - 2)
3 2β
4 β
5
2 β
0.0
0
200
400
600
800
t (s)
γ
kˆ = k +
m+
c
β Δt
β Δt 2
1
1.5x106
Ri +1 = Pi +1 + m(a0ui + a2ui + a3ui ) + c (a1ui + a4ui + a5ui )
1.0x10
Displacement at time step i+1
5.0x105
Level 3
Level 7
Fyj (N)
6
ˆ
Ku
i +1 = Ri +1
0.0
-5.0x105
Acceleration and velocity at time step i+1
1
1
1
ui +1 =
u + (1(u -u ))ui
βΔt 2 i +1 i βΔt i
2β
γ
γ
γ
ui +1 = (1- )ui +
(ui +1 -ui ) + (1)ui Δt
2β
β
β Δt
-1.0x106
-1.5x106
0
200
400
600
800
t (s)
i<n
Level 3
Level 7
6.0x106
u u u
Mzj (N·m)
Output
9.0x106
End
Fig. 5. Flow chart of the Newmark method.
3.0x106
0.0
-3.0x106
acceleration at time step i (i+1) respectively, Δt is the interval of every
time step, the factors β and γ define the variation of acceleration over a
time step and determine the stability and accuracy characteristics of the
method. In the present paper, the constant average acceleration method
is used, and the value of β and γ are determined to be 1/2 and 1/4
respectively. The flow chart of the Newmark method is shown in Fig. 5.
-6.0x106
-9.0x106
0
200
400
t (s)
600
800
Fig. 6. Time history of wind excitations of the square tall building.
3.2. Determination of wind excitation
sampling frequency is 625 Hz in the wind tunnel test, the time step for
the wind-induced response analysis can be determined to be 0.0776 s,
and the total time is 12.93 min after 10,000 time steps of calculation.
The time history of wind excitations at j story of each simplified
mass-spring model (see Section 3.4) can be calculated by Eqs. (7)–(9),
and the along-wind, across-wind and torsional wind excitations on two
selected stories of the square tall building (Model 1) are shown in Fig. 6.
According to GB 50009-2012 [40], the basic wind pressure (defined
in the exposure category B) in Harbin city of China is 0.55 kN/m2. So
the oncoming wind speed at top of the tall building (180 m) in the
exposure category C can be determined to be 43.35 m/s. Therefore, the
wind speed ratio between the scaled model and the prototype building
Um/Up is 7/43.35 equal to 1/6.19. Assume the geometric scale ratio
between the scaled model and prototype tall building Bm/Bp is 1/300,
so the frequency ratio fm/fp can be determined to be 48.47. As the
90
Engineering Structures 175 (2018) 86–100
C. Zheng et al.
Fig. 7. FEM of the prototype tall building: (a) plan and (b) elevation.
Fxj (t ) =
1
ρ UH2 hj B xj CFxj (t )
2 ∞
(7)
Fyj (t ) =
1
ρ UH2 hj B yj CFyj (t )
2 ∞
(8)
Mzj (t ) =
1
ρ UH2 hj B xj B yj CMzj (t )
2 ∞
building, its damping ratio is 0.02 for all modes.
Fig. 8 shows the first 6 orders of natural frequency and modal shape
of the prototype tall building. It can be seen that Modes 1 & 2 and
Modes 4 & 5 are the vibrations in the lateral directions with a natural
frequency of 0.218 Hz and 0.697 Hz respectively; and Mode 3 and
Mode 6 are the vibrations in the rotational direction with a natural
frequency of 0.293 Hz and 0.849 Hz respectively.
(9)
where Fxj(t), Fyj(t), and Mzj(t) are the wind forces in the x and y directions, and the torsional moment around the z direction respectively; hj
is set as the height of the j story; Bxj and Byj are the transverse width
normal to the x and y directions at the j story; CFxj(t), CFyj(t) and CMzj(t)
are time history of the force coefficient in the x and y directions, and the
torsional moment coefficient at the j story of each prototype tall
building or simplified mass-spring model.
3.4. Simplified mass-spring model
As the time history analysis of wind-induced responses for the
prototype tall building is quite time consuming, a simplified massspring model is introduced to improve the computational efficiency but
with enough accuracy. As is shown in Fig. 9, the prototype tall building
used in Section 3.3 is simplified as a 10-story model with lumped
masses and springs using ANSYS 14.0, in which every 6-story of the tall
building are condensed into a point with mass (mi) and torsional moment of inertia (Ii), and a link with two lateral springs in x and y directions (whose stiffness is kx and ky respectively), a torsional spring
(whose stiffness is kz) and a damper (whose damping constant is c). The
mass and the torsional moment of inertia are modeled by a MASS21
element, and the lateral springs, torsional springs and dampers are
modeled by a COMBIN14 element.
The total mass of the simplified mass-spring model is 135432 t,
which is very close to that of the prototype tall building (135322 t). The
comparison of the first 6 orders of natural frequency between the
prototype tall building and the simplified mass-spring model is listed in
Table 3, it can be seen that the deviations for the first 3 orders of frequency are all 0. Fig. 10 compares the first 3 orders of standardized
modal shapes between the prototype building and the model, and a
good agreement is found for the lateral and torsional modal shapes,
3.3. Prototype tall building
As is shown in Fig. 7, the finite element model (FEM) of a steel
braced frame structure with 60 stories and 6 bays in the plan is constructed using ANSYS 14.0, to simulate the prototype tall building with
square cross-section (corresponds to Model 1). Dimensions of each story
are 35.4 × 35.4 × 3 m3 with a uniform bay spacing of 5.9 m, so the
total height of the tall building is 180 m. The steel braced frame
structure consists of steel beams, ordinary steel columns and reinforced
steel columns, chevron concentrically steel braces and steel slabs, and
dimensions of these components are listed in Table 2. It can be seen that
the columns have a box cross-section, and the beams and braces have an
I-shaped cross-section. The columns and beams are modeled using the
Beam188 Element, and the braces and slabs are modeled using the
Link180 and Shell63 Elements respectively. The modulus of elasticity of
steel is 210 GPa, and its yielding stress is 235 MPa. For the steel tall
Table 2
Dimensions of the components of the prototype tall building (Unit: mm).
Stories
Ordinary columns (Beam188)
Reinforced columns (Beam188)
Beams (Beam188)
Braces (Link180)
Slabs (Shell63)
1-20
21-40
41-60
□1000 × 1000 × 50
□900 × 900 × 40
□600 × 600 × 35
□1500 × 1500 × 60
□1100 × 1100 × 50
□700 × 700 × 40
I700 × 300 × 12 × 30
I700 × 300 × 12 × 30
I700 × 300 × 12 × 30
I300 × 400 × 10 × 20
I300 × 400 × 10 × 20
I300 × 400 × 10 × 20
5900 × 5900 × 200
5900 × 5900 × 200
5900 × 5900 × 200
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Engineering Structures 175 (2018) 86–100
C. Zheng et al.
Fig. 8. The first 6 modes of the prototype tall building: (a) Modes 1 & 2 with a frequency of 0.218 Hz, (b) Mode 3 with a frequency of 0.293 Hz, (c) Modes 4 & 5 with a
frequency of 0.697 Hz, (d) Mode 6 with a frequency of 0.849 Hz.
especially for the 3rd mode (the torsional mode). Considering the
contributions to the structural wind-induced responses caused by the
first 3 modes are dominant, so it can be concluded that the simplified
mass-spring model can accurately simulate the dynamic properties of
the prototype tall building.
Besides the dynamic properties, the extremum tip displacements in
the lateral and torsional directions of the simplified mass-spring model
under a wind direction angle of 0° are also compared with those of the
prototype tall building (Model 1) in Fig. 11. The extremum displacement ue can be calculated by Eq. (10).
ue = u + sign (u ) × g × σu
Table 3
Comparison of natural frequency between prototype tall building and simplified
mass-spring model.
Mode
Freq. of prototype tall
building (Hz)
Freq. of simplified massspring building (Hz)
Deviation/%
1
2
3
4
5
6
0.218
0.218
0.293
0.697
0.697
0.849
0.218
0.218
0.293
0.580
0.580
0.839
0%
0%
0%
16.8%
16.8%
1.2%
(10)
increases, the trend of the extremum tip displacements of the two
models is the same, and their values are close to each other, with a
maximum deviation of 5.8%, 4.8% and 17% for the along-wind, acrosswind and torsional displacements respectively. However, the
where u and σu are the mean displacement and root mean square (RMS)
of displacement respectively, g is the peak factor as set as 2.5 in this
paper, and sign() is the sign function.
It can be seen in Fig. 11 that, as the suction flux coefficient CQ
Fig. 9. Schematic diagram of the mass-spring model.
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Engineering Structures 175 (2018) 86–100
C. Zheng et al.
Standardized height (z/H)
1.0
the Y-shaped tall building), with a proportion of 34% and 30% respectively. The results are quite close to Kwok et al.’s research on the
maximum reduction of along-wind tip displacement of the CAARC tall
building (40%) caused by chamfered corners [41], and are slightly
larger than Elshaer et al.’s study on the maximum reduction of the
along-wind responses (29%) of a 120 m tall building generated by the
aerodynamic optimization for corner modifications [12]. The above
comparisons indicate that the experimental and analysis results of the
tall building controlled by shape optimization of the cross-section in the
present paper are within expected results.
As CQ increases, the extremum tip displacement of Model 1 in
Fig. 12a first decreases slightly and then increases significantly under a
relative low CQ (e.g. CQ ≤ 0.0161), and then decreases gradually under
larger CQ (e.g. CQ ≥ 0.0203). And the reason can be attributed to the
flow field caused by the suction control [34], which can be expressed as
follows: Firstly, suction control removes low-speed flows in the
boundary layer and deflects flows towards the side faces, so the width
of the recirculation region will be reduced, resulting in a reduction of
the drag force and the corresponding along-wind displacement. Secondly, the length of the recirculation region will also be reduced due to
the suction control, so the negative pressure on the leeward face will be
enlarged, resulting in an increased drag force and along-wind displacement. Maybe the second aspect is dominant for Model 1 under a
low CQ, while the first aspect tends to take over under a large CQ. The
maximum reduction of the extremum tip displacement of Model 1,
which is caused by the suction control, can reach to 22% when CQ
equals to 0.0365.
As for Models 2–3, their extremum tip displacements show a trend
in reduction when CQ increases, while it is not varied for Model 4. The
maximum reduction of the tip displacement of Models 2–3 caused by
the suction control can reach to 29% and 27% respectively when CQ
equals to 0.0356. Therefore, the maximum total reduction of the tip
displacement for Models 2–3, which is caused by the combined aerodynamic control, can reach to 63% and 51% respectively, indicating
that the effect of the combined aerodynamic control is very significant.
The along-wind RMS tip accelerations in Fig. 12b have the same
trend with those of the extremum tip displacements in Fig. 12a. The
maximum reduction of the RMS tip acceleration caused by combined
aerodynamic control also belongs to Model 2, with a proportion of 58%
(28% caused by shape optimization and 30% caused by air suction
respectively).
Based on the above statements, it can be concluded that the reduction of the along-wind extremum displacement and RMS tip acceleration (63% and 58% for Model 2) caused by the combined aerodynamic control in the present paper are significantly larger than those
acquired by some previous researchers, such as a reduction of the
along-wind extremum displacement and RMS tip acceleration up to
43% and 51% for a 400 m super-tall building caused by using a new
combined structural system [42], and 39% and 49% caused by using a
1000 t TMD [42]; and a reduction of the RMS tip acceleration up to
30% for the Shanghai World Financial Center (492 m) by using two
TMDs with a total mass of 253 t [43], and about 28% for a 180 m tall
building by using a pair of TLDs [44]. The above comparisons can in
some extent indicate the effectiveness of the combined aerodynamic
control to mitigate the along-wind responses of tall buildings.
The along-wind extremum tip displacements of Models 1–4 at different wind direction angles θ are shown in Fig. 13. When there is no
suction control (see Fig. 13a), the extremum tip displacement of Model
1 shows a slight decrease as θ increases, and the maximum value occurs
when θ equals to 0°. However, for other models, the extremum tip
displacement shows a sharp increase as θ increases, and the maximum
value occurs when θ equals to 30° for Models 2 & 4 and 45° for Model 3.
Furthermore, the shape optimization can reduce the tip displacements
when θ is less than or equal to 30°, and among them Model 4 has the
best wind-resistance performance. When there is suction control (see
Fig. 13b), the above regularities are also observed for these Models
Modes 1 & 2 - prototype
Modes 1 & 2 - model
Mode 3 - prototype
Mode 3 - model
0.8
0.6
0.4
0.2
0.0
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Standardized modal shape
Along-wind displacement - model
Along-wind displacement - prototype
Across-wind displacement - model
Across-wind displacement - prototype
140
3.0x10-3
2.5x10-3
120
2.0x10-3
100
1.5x10-3
80
Torsional displacement - model
Torsional displacement - prototype
1.0x10-3
60
0.00
0.01
0.02
0.03
Extremum tip torsional displacement (rad)
Extremum tip displacement (mm)
Fig. 10. Comparison of standardized modal shapes for prototype tall building
and simplified mass-spring model.
0.04
CQ
Fig. 11. Comparison of the extremum tip displacements between the simplified
mass-spring model and prototype tall building.
computational efficiency for the time history analysis has been much
improved by using the simplified mass-spring model, as its computational time for 10,000 time steps is about 1 h, which is much less than
12 h of the prototype tall building.
It should be noted that, it is the aim to investigate the effect of the
combined aerodynamic control on the wind-induced responses of tall
buildings in the present paper, so the dynamic properties of the four tall
buildings (i.e. the prototype tall buildings for Models 1–4) are assumed
to be same. Therefore, though the simplified mass-spring model is established for the prototype tall building with square cross-section in
Section 3.3, it can also be used to calculate the wind-induced responses
of other tall buildings.
4. Results analysis
4.1. Along-wind responses
Fig. 12 shows the relationship between the extremum tip displacements together with RMS tip accelerations in the along-wind direction
and the suction flux coefficient CQ for different simplified mass-spring
models. The wind direction angle θ is set as 0°. It can be seen in Fig. 12a
that, when there is no air suction (CQ = 0), the reduction of the tip
displacement caused by the shape optimization is very significant for
Model 2 (i.e. the corner-recessed square tall building) and Model 4 (i.e.
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Engineering Structures 175 (2018) 86–100
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140
Model 1
Model 2
120
Model 3
Model 4
RMS tip acceleration (mm·s-2)
Extremum tip displacement (mm)
C. Zheng et al.
100
80
60
40
Model 3
Model 4
35
30
25
20
15
10
20
0.00
(a)
Model 1
Model 2
40
0.01
0.02
0.03
0.04
0.00
(b)
CQ
0.01
0.02
0.03
0.04
CQ
Fig. 12. Along-wind (a) extremum tip displacements and (b) RMS tip accelerations under different CQ.
the structural frequency, has a narrow bandwidth with large amplitude.
It can be seen in Fig. 14a that, the background and resonant components of Model 1 both increase at a low CQ (CQ = 0.0161) and then
decrease at a large CQ (CQ = 0.0365), indicating that the suction
control can only be effective in reduction of the along-wind response for
Model 1 when CQ is large enough. This phenomenon can also be observed in Fig. 12. For the tip displacement spectrum of Model 2 (see
Fig. 14b), its magnitude is much less than that of Model 1 for both the
background and resonant components, indicating that the effect of
shape optimization is very significant. Besides, it is clearly illustrated
that the background and resonant components are further reduced by
the air suction, but the control effect will be not obvious when CQ is
larger than 0.0159.
The different trends of the effect of CQ on the PSD in Fig. 14a and b
indicate the mechanism of suction control may be slightly different for
Model 1 and Model 2, and it can be inferred that the location of the
reattachment of separated flows will account for it. Firstly, as the
leading edge of the side face for Model 1 is much sharper than that for
Model 2, and also the after-body length of Model 1 is relatively larger
than that of Model 2, the vortex shedding for the former model will be
more significant. Secondly, for Model 1, as the suction control can
deflect the separated flows and promote their reattachment, most of the
separated flows will reattach at the recirculation region with a dramatic
fluctuation when CQ is small (e.g. CQ equals to 0.0161 in Fig. 14a), and
110
Extremum tip displacement (mm)
Extremum tip displacement (mm)
except for Model 1, whose extremum tip displacement shows a slight
increase as θ increases. Moreover, the combined aerodynamic control
can also reduce the extremum tip displacements when θ is less than 30°.
After comparison of the tip displacements with and without suction
control, it can be clearly identified that the suction control can sometimes enlarge the displacements at large wind direction angles, e.g. θ
equals to 45° for Model 1, and θ equals to 30° for Models 2–3. And the
reason can be attributed to that: When it is at large wind direction
angle, the suction control will be operated in the leeward face, so the
vortices near the face will be regenerated due to the air suction, and
also the wake length will be reduced. Therefore, the above reason can
result in an increase of the extremum tip displacements for the models.
However, the effect of suction control on the tip displacements of Model
4 is different from the above analysis, because the suction control has
already operated in the leeward face at a small oblique wind direction
(θ < 30°).
The power spectra density (PSD) for the fluctuating tip displacements of Models 1–2 under different CQ are shown in Fig. 14. The wind
direction angle is set as 0°. The standard deviation of the tip displacement, which can be calculated by summation of the areas below each
curve, can be further divided into the background and resonant components. The background component represents the quasi-static response caused by the gust spectrum with a broad bandwidth; and the
resonant component, which is related to the magnified response near
100
(a)
90
80
Model 1
Model 2
Model 3
Model 4
70
60
0
15
30
45
60
(b)
θ (°)
120
100
80
60
Model 1
Model 2
Model 3
Model 4
40
20
0
15
30
θ (°)
Fig. 13. Along-wind extremum tip displacements at different θ: (a) Uc = 0 m/s, and (b) Uc = 9 m/s.
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3000
8000
CQ=
0
0.0159
0.0356
2000
2
S( f ) (m ·s)
6000
S( f ) (m2·s)
CQ=
0
0.0161
0.0365
4000
1000
2000
0
(a)
0
0.01
0.1
f (Hz)
1
0.01
(b)
0.1
f (Hz)
1
Fig. 14. Along-wind tip displacement spectra of (a) Model 1 and (b) Model 2 under different CQ.
the across-wind direction can also be restrained due to a less circulation
to generate the flow separation at the leading edge and a short afterbody length to develop the vortices, resulting in a significant reduction
of the across-wind displacements.
As CQ increases, the extremum displacements decrease dramatically
for Model 1 and show a tendency to decrease for Model 2, indicating
that a larger CQ can lead to a better control effect on the across-wind
responses. However, the above regularity is changed for Models 3–4. As
CQ increases, the responses decrease first and then increase for Model 3,
and it shows no obvious change of the across-wind responses for Model
4. The maximum reduction of the extremum tip displacement reaches
47% for Model 1, and 53% for Models 2–3 and 58% for Model 4. It
should be noted that the reduction of the across-wind displacements for
Models 2–4 caused by air suction are much less than that for Model 1
(47% when CQ equals to 0.0365), especially for Model 4 with a proportion of only 9% when CQ equals to 0.0135. The above results indicate that the vortex shedding for Models 2–4 has already been substantially restrained by the shape optimization, and hence the reduction
of the across-wind displacement generated by air suction will not be
very significant compared to the baseline model (Model 1).
The across-wind RMS tip accelerations in Fig. 15b have the same
trend with those of the extremum tip displacements in Fig. 15a. The
maximum reduction of RMS acceleration reaches 40% for Model 1
when CQ equals to 0.0365, and 62% for Models 2–3 and 69% for Model
4.
will reattach at the side faces with a reduced wake width when CQ is
large (e.g. CQ equals to 0.0365 in Fig. 14a). While for Model 2, due to
the less significant vortex shedding, the reattachment of separated
flows at the side faces will be promoted, resulting in a reduction of drag
force and corresponding along-wind fluctuating displacement.
4.2. Across-wind responses
120
140
Model 1
Model 2
Model 3
Model 4
RMS tip acceleration (mm·s-2)
Extremum tip displacement (mm)
Fig. 15 shows the relationship between the extremum tip displacements together with RMS tip accelerations in the across-wind direction
and the suction flux coefficient CQ for Models 1–4. The wind direction
angle θ is set as 0°. It can be seen in Fig. 15a that, when there is no air
suction (CQ = 0), the reductions of the across-wind tip displacements
caused by the corner recession (Model 2) and corner-chamfering
(Model 2) are both very significant, with a proportion of 39%. The
above reductions are slightly larger Kwok et al.’s research on the
maximum reduction of crosswind tip displacement of the CAARC tall
building (30%) caused by chamfered corners [41], which further indicates the experimental and analysis results in the present paper are
accurate. The reduction of the tip displacement caused by the Y-shaped
geometry (Model 4) is the most significant, with a proportion of 49%.
Therefore, Model 4 shows the best wind-resistance performance in the
across-wind direction; and the reason can be attributed to a significant
restraint of vortex shedding due to the gradually increased frontal area
downstream the side face. While for Models 2–3, the vortex shedding in
120
100
80
60
100
Model 3
Model 4
80
60
40
20
0.00
(a)
Model 1
Model 2
0.01
0.02
CQ
0.03
0.04
0.00
(b)
0.01
0.02
CQ
Fig. 15. Across-wind (a) extremum tip displacements and (b) RMS tip accelerations under different CQ.
95
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Engineering Structures 175 (2018) 86–100
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Extremum tip dispalcement (mm)
Extremum tip dispalcement (mm)
C. Zheng et al.
Model 1
Model 2
Model 3
Model 4
120
100
80
60
40
20
(a)
0
15
30
45
60
160
140
100
80
60
40
(b)
(°)
Model 1
Model 2
Model 3
Model 4
120
0
15
30
45
60
(°)
Fig. 16. Across-wind extremum tip displacements at different θ: (a) Uc = 0 m/s, and (b) Uc = 9 m/s.
CQ on the across-wind fluctuating displacements is not very obvious
when CQ is larger than or equal to 0.0159, which is similar to the alongwind fluctuating displacements in Fig. 14b.
Based on the above statements, it can be concluded that the reduction of the across-wind extremum displacement and RMS tip acceleration caused by combined aerodynamic control (58% and 69% for
Model 4) in the present paper are significantly larger than the reduction
of the across-wind extremum displacement (41%) and slightly larger
than the reduction of the RMS tip acceleration (65%) for a 400 m supertall building caused by using a new combined structural system [42],
and are significantly larger than those reductions (32% and 54%) for
the same building caused by using a 1000 t TMD [42]. And these
comparisons further indicate the combined aerodynamic control may
be more effective than some other measures (such as the new combined
structural system and TMD in [42]) to mitigate the wind-induced responses of tall buildings.
The across-wind extremum tip displacements of Models 1–4 at different wind direction angles are shown in Fig. 16. When there is no
suction control (see Fig. 16a), the maximum extremum tip displacement
of Model 1 shows a sharp decrease as θ increases; while the extremum
tip displacements of Models 2–4 increase first and then decrease as θ
increases, and the maximum value occurs when θ equals to 15° for
Models 2–3 and θ equals to 30° for Model 4. Furthermore, reduction of
the tip displacements due to the shape optimization is only effective
when θ equals to 0°, and among them Model 4 has the best wind-resistance performance. The above results imply that the passive aerodynamic control is sometimes only effective in a limited wind direction
angles, when the actual situation slightly deviates from the expected
condition, the control effect is often not in the best state or even unfavorable to the structure’s performance [26].
When there is suction control (see Fig. 16b), due to the air suction,
the most unfavorable wind direction angles are postponed for Models
1–2 and changed from 30° to 15° for Model 4. Moreover, only the wind
direction that θ equals to 0° can be observed to have a considerable
improvement of the wind-resistance performance for the models under
the combined aerodynamic control.
Fig. 17 shows the PSD for the across-wind fluctuating tip displacements of Models 1–2 under different CQ. The wind direction angle is set
as 0°. It can be illustrated in Fig. 17a that, due to the air suction, the
resonant component decreases dramatically and the background component increases slightly for Model 1, and the larger CQ is, the better
control effect is. For the displacement spectrum of Model 2 in Fig. 17b,
its resonant magnitude is much less than that of Model 1 without suction control, indicating that the combination of the corner recession and
air suction is very effective in reduction of the resonant responses.
Besides, the resonant component decreases dramatically due to the air
suction, but the background component increases a lot. So the effect of
4.3. Torsional responses
Effect of CQ on the extremum tip torsional displacements of Models
1–4 are shown in Fig. 18. The wind direction angle θ is set as 0°. It can
be seen that, when there is no air suction, the torsional displacements
can be considerably reduced by the shape optimization, especially for
Model 4; however, when the air suction is added, the torsional displacements of Models 1–3 increase as CQ increases, indicating that the
suction control would be unfavorable to the wind-resistance performance in the torsional direction. And the reason can be attributed to the
fact that the air suction through the two suction holes, which are far
from center of the building (see Fig. 3), will generate a large quantity of
unsteady small vortices around the hole, so as to increase the torque
moment. The larger the CQ is, the more significant the torque moment
is. While for Model 4, the influence of suction control on its torsional
response seems to be not obvious.
The extremum tip torsional displacement of Model 1 under CQ of
0.0323 is about 1.9 times larger than that of the model without suction
control. Although the magnitude of torsional displacement is quite
small when compared to the along-wind and across-wind displacements
in Figs. 12a and 15a respectively, it still should be careful to utilize the
suction control for the buildings with a non-symmetric cross-sectional
shape or mass and stiffness eccentricity.
Fig. 19 presents the extremum tip torsional displacements at different wind direction angles. When there is no suction control (see
Fig. 19a), the most unfavorable wind direction angles are 0°, 15°, 15°,
30° for Models 1–4 respectively. And the passive aerodynamic control
can significantly reduce the tip displacements when θ is less than 45°,
especially for Model 4. When the models are controlled by air suction
with a suction speed Uc of 9 m/s (see Fig. 19b), the most unfavorable
wind direction angles will be shifted to 15°, 0°, 0°, 15° for Models 1–4
respectively. Similarly to Figs. 18 and 19a, Model 4 is the most effective
in suppressing the torsional displacement, while the suction control
almost has no effect.
The PSD for the fluctuating tip torsional displacements of Models
1–2 are shown in Fig. 20. It can be illustrated that, as CQ increases, the
background and resonant components both increase for Model 1, while
the background component decreases and the resonant component increases for Model 2. The opposite results in the background component
for Model 1 and Model 2 may result from the different locations of the
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Engineering Structures 175 (2018) 86–100
C. Zheng et al.
70000
60000
20000
S( f ) (m2·s)
S( f ) (m2·s)
50000
C Q=
40000
0
0.0161
0.0365
30000
CQ=
0
0.0159
0.0356
10000
20000
10000
0
0
0.01
(a)
0.1
f (Hz)
1
(b)
0.01
0.1
f (Hz)
1
Torsional extremum tip displacement (rad)
Fig. 17. Across-wind tip displacement spectra of (a) Model 1 and (b) Model 2 under different CQ.
2.4E-03
Model 1
Model 2
2.0E-03
control on the wind-induced responses of tall buildings, three values,
including value 1, value 2, value 3, are defined by Eqs. (11)–(13) to
quantitatively express the reduction of the responses caused by the
passive aerodynamic control (shape optimization), active aerodynamic
control (air suction) and combined aerodynamic control respectively.
Model 3
Model 4
1.6E-03
value 1 =
r b−rp
value 3 =
(11)
rb
1.2E-03
r b−rp+a
8.0E-04
(12)
rb
(13)
value 2 = value 3−value 1
4.0E-04
where rb represents the wind-induced response of the baseline model
(Model 1) without suction control, and rp and rp+a represent the windinduced response of tall buildings controlled by the passive aerodynamic control and combined aerodynamic control respectively.
When the value 2 is positive, it means that the suction control can reduce the wind-induced response, and vice versa.
The value 1, maximum (when air suction can reduce the wind-induced response) or minimum (when air suction can increase the windinduced response) value 2 and value 3, and the corresponding CQ for
Models 1–4 are listed in Table 4 respectively. The wind direction angle
is set as 0°, and the response is the extremum tip displacement of tall
buildings.
It can be seen in Table 4 that, in the along-wind direction, the
maximum reduction of the extremum tip displacement caused by the
0.0E+00
0.00
0.01
0.02
CQ
0.03
0.04
Fig. 18. Extremum tip torsional displacement under different CQ.
separated flows’ reattachment, which is similar to the PSD in Fig. 14.
5. Discussions
Extremum tip torsional displacement (rad)
Extremum tip torsional displacement (rad)
In order to intuitively show the effect of the combined aerodynamic
1.2E-03
Model 1
Model 2
Model 3
Model 4
1.0E-03
8.0E-04
6.0E-04
4.0E-04
2.0E-04
0.0E+00
0
(a)
15
30
(°)
45
60
2.4E-03
Model 1
Model 2
Model 3
Model 4
2.0E-03
1.6E-03
1.2E-03
8.0E-04
4.0E-04
0.0E+00
0
(b)
15
30
(°)
Fig. 19. Extremum tip torsional displacement at different θ: (a) Uc = 0 m/s, and (b) Uc = 9 m/s.
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Engineering Structures 175 (2018) 86–100
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5.0E-06
2.0E-06
0
0.0161
0.0365
3.0E-06
2
S( f ) (rad ·s)
S( f ) (rad2·s)
C Q=
CQ =
4.0E-06
2.0E-06
0
0.0159
0.0356
1.0E-06
1.0E-06
0.0E+00
0.01
0.1
(a)
0.0E+00
0.01
1
f (Hz)
0.1
(b)
1
f (Hz)
Fig. 20. Tip torsional displacement spectra of (a) Model 1 and (b) Model 2 under different CQ.
Table 4
Value 1, value 2, value 3 and corresponding CQ for Models 1–4 under combined aerodynamic control.
Model
Model
Model
Model
Model
Along-wind response
1
2
3
4
Across-wind response
Torsional response
Value 1, value 2, value 3
CQ
Value 1, value 2, value 3
CQ
Value 1, value 2, value 3
CQ
0, 0.22, 0.22
0.34, 0.29, 0.63
0.24, 0.27, 0.51
0.30, 0, 0.30
0.0365
0.0159
0.0356
0
0, 0.47, 0.47
0.39, 0.14, 0.53
0.39, 0.13, 0.52
0.49, 0.09, 0.58
0.0365
0.0356
0.0198
0.0135
0, −0.91, −0.91
0.45, −0.30, 0.15
0.49, −0.59, −0.10
0.60, −0.16, 0.44
0.0323
0.0356
0.0323
0.0162
Eqs. (14) and (15) to express the maximum and minimum reduction of
the responses caused by the shape optimization and combined aerodynamic control respectively at all the wind direction angles. As the
wind-induced responses of the baseline model (Model 1) reach to the
maximum values at wind direction angle of 0° (see Figs. 13a, 16a, 19a),
the wind-induced response at 0° (rb,θ=0) is adopted as the baseline value
in the equations.
shape optimization, air suction and combined aerodynamic control are
all belonged to Model 2, with a proportion of 34%, 29% and 63% respectively, and the optimal suction flux coefficient CQ is 0.0159. In the
across-wind direction, the maximum reduction of the extremum tip
displacement caused by the shape optimization and combined aerodynamic control are both belonged to Model 4, with a proportion of
49% and 58% respectively, and the maximum reduction of the displacement caused by air suction belongs to Model 1 with a proportion
of 47%. Furthermore, for the tip torsional displacements, it can be illustrated that a significant reduction of them is caused by the shape
optimization, with a maximum reduction of 60% for Model 4. However,
the air suction will increase torsional displacements, and the maximum
increase of the torsional displacement occurs at Model 1 with a proportion of 91%.
Besides, according to the above statements in Section 4, the effect of
combined aerodynamic control on the wind-induced responses will be
quite different when θ varies. So the value 4 and value 5 are defined by
value 4 =
r b, θ = 0−min{rθ |θ = 0°, 15°, 30°, 45°, 60°}
r b, θ = 0
(14)
value 5 =
r b, θ = 0−max{rθ |θ = 0°, 15°, 30°, 45°, 60°}
r b, θ = 0
(15)
where rθ represents the wind-induced response of Models 1–4 at different
wind direction angles, and rθ can be used to express the wind-induced
response of tall buildings controlled by the passive aerodynamic control
rp and combined aerodynamic control rp+a respectively.
Table 5
Value 4, value 5 and corresponding θ for Models 1–4 with/without suction control.
Model
Uc = 0 m/s
Along-wind response
Across-wind response
Torsional response
Uc = 9 m/s
Along-wind response
Across-wind response
Torsional response
Model 1
Model 2
Model 3
Model 4
Value 4 and corresp. θ
0.06, 45°
0.34, 0°
0.24, 0°
0.31, 15°
0.02,
0.59,
0.39,
0.70,
0.23,
0.07,
0.59,
0.41,
0.67,
0.59,
30°
60°
30°
60°
30°
0.22,
0.06,
0.58,
0.28,
0.68,
0.51,
0°
30°
60°
15°
45°
15°
Value
Value
Value
Value
Value
5
4
5
4
5
and
and
and
and
and
corresp.
corresp.
corresp.
corresp.
corresp.
θ
θ
θ
θ
θ
0, 0°
0.69, 45°
0, 0°
0.66, 45°
0, 0°
0.08,
0.58,
0.37,
0.61,
0.23,
Value
Value
Value
Value
Value
Value
4
5
4
5
4
5
and
and
and
and
and
and
corresp.
corresp.
corresp.
corresp.
corresp.
corresp.
θ
θ
θ
θ
θ
θ
0.21, 0°
−0.06, 45°
0.63, 45°
0.23, 15°
0.57, 45°
−1.15, 15°
0.63, 0°
0, 30°
0.60, 45°
−0.10, 30°
0.47, 45°
0.12, 30°
98
30°
30°
15°
45°
15°
45°
45°
15°
45°
15°
0.51, 0°
−0.10, 45°
0.52, 45°
0.29, 15°
0.60, 45°
−0.06, 0°
Engineering Structures 175 (2018) 86–100
C. Zheng et al.
Table 5 shows the value 4, value 5 and the corresponding θ for
Models 1–4 with suction control (Uc = 9 m/s) and without suction
control (Uc = 0 m/s). For Model 1 without air suction, the maximum
reduction of the responses (value 4) caused by wind direction angles can
reach to 0.06, 0.69 and 0.66 in the along-wind, across-wind and torsional directions respectively, and the most unfavorable wind direction
angle is 0°. However, when Model 1 is under air suction (Uc = 9 m/s),
its most unfavorable wind direction angle is almost shifted to 15°. For
Models 2–3, the most unfavorable wind direction angle is almost shifted
from 15° to 30° when the air suction is added, and the maximum reduction of the responses is quite considerable. For Model 4, though the
most unfavorable wind direction angle is decreased due to air suction,
the reduction of the torsional responses is quite large at all wind direction angles.
This paper discusses the influences of the combined aerodynamic
control on wind-induced responses of a tall building with a specific
dynamic property (see Sections 3.3 and 3.4). For the tall buildings with
different dynamic properties, such as the natural frequency, modal
shape, and damping ratio, influence of the combined aerodynamic
control on the wind responses is still an issue for future research, and
are not discussed in this paper due to the limited space.
unfavorable to the torsional responses. The torsional displacement
of Model 1 under CQ of 0.0323 is about 1.9 times larger than that of
the model without suction control. However, the maximum reduction of the torsional responses caused by the combined aerodynamic
control can still be very considerable at different wind direction
angles, with a value of 0.57, 0.47, 0.60 and 0.68 for Models 1–4
respectively when Uc equals to 9 m/s.
This study contributes to a new aerodynamic control strategy for the
designers to look for a solution to the wind-resistance design of tall
buildings, especially for a particularly challenging project.
Acknowledgement
The authors want to express their appreciation for the financial
support provided by the National Natural Science Foundation of China
(Nos. 51578186 and 51108142).
Appendix A. Supplementary material
Supplementary data associated with this article can be found, in the
online version, at https://doi.org/10.1016/j.engstruct.2018.08.031.
6. Conclusions
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Characteristics of wind-induced responses of a tall building under
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of the cross-section (includes the square, corner-recessed square,
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of the shape optimization, air suction and combined aerodynamic
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studies and potential engineering applications of the combined aerodynamic control in the wind-resistance design of tall buildings. The
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